Non-minimum phase FIR system identification using cumulants with selected orders

In this paper, we address the problem of identifying the parameters of a nonminimum phase FIR system from the cumulants of some noisy output samples. The system is driven by an unobservable, zero-mean, independent and identically distributed (i.i.d) non-Gaussian signal. The measurement noise may be coloured MA or ARMA Gaussian process. For this problem, there have been a number of linear cumulant-based approaches. But these algorithms fail to perform the estimation due to using the correlation of outputs. In this paper, we propose two methods, one is to employ two arbitrary adjacent order cumulants, while the other is to use two arbitrary order cumulants together with the cumulant with the order equal to the sum of the orders of the two arbitrary cumulants. Simulation experiments, by comparing our algorithms with other existing algorithms, prove that the first algorithm indeed produces the best estimates in terms of the mean, the standard deviation and the root mean-square error of the parameter estimates when the signal-to-noise ratio is very small